In this work we extend our earlier analysis of the novel Josephson effect in triplet superconductor-ferromagnet-triplet superconductor (TFT) junctions [Kastening et al., Phys. Rev. Lett. 96, 047009 (2006)]. In our more general formulation of the TFT junction, we allow for potential scattering at the barrier and an arbitrary orientation of the ferromagnetic moment. Several new effects are found upon the inclusion of these extra terms: for example, we find that a Josephson current can flow even when there is vanishing phase difference between the superconducting condensates on either side of the barrier. The critical current for a barrier with magnetization parallel to the interface is calculated as a function of the junction parameters, and is found to display strong nonanalyticities. Furthermore, the Josephson current switches identified in our previous work are found to be robust features of the junction, while the unconventional temperature dependence of the current is very sensitive to the extra terms in the barrier Hamiltonian.